The system of equations:
y = 5x + 10
y = 5x + 2
Has no solutions. There are several ways to explain why. We'll give the following:
Each equation corresponds to a line of slope m = 5 (the coefficient of x) but they are not the same line because the y-intercept of the lines is different. This means we have two parallel lines and they will never meet. So there is no solution for the system.
If we equate y on both equations, we have:
5x + 10 = 5x + 2
Simplifying by 5x:
10 = 2
We obtain a false condition, the equation is false and we cannot find any solutions. If the equation were true, we would have infinitely many solutions
Answer: No solution